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1999 | 19 | 1-2 | 45-65
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On the solution set of the nonconvex sweeping process

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We prove that the solutions of a sweeping process make up an $R_δ$-set under the following assumptions: the moving set C(t) has a lipschitzian retraction and, in the neighbourhood of each point x of its boundary, it can be seen as the epigraph of a lipschitzian function, in such a way that the diameter of the neighbourhood and the related Lipschitz constant do not depend on x and t. An application to the existence of periodic solutions is given.
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  • Dipartimento di Matematica Pura e Applicata, Universita di Modena, via Campi 213/B, 41100 Modena, Italy
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